علی حاجی بدلی

In this paper we considered non-reductive homogeneous pseudo Riemannian manifolds of dimension four and investigated recurrent curvature tensor condition for those curvature tensor. We classified non-reductive homogeneous pseudo Riemannian manifolds with recurrent curvature tensor, and in the other cases, admitting the recurrent curvature tensor condition is equivalent to be locally symmetric or flat curvature tensor and only for one case we have not any 1-form so that satisfy in recurrent curvature tensor. Then we investigated some geometrical concepts for them like Weyl tensor, Einstein property and etc., we obtained some results, for example we show when any non-reductive homogeneous manifold with recurrent curvature tensor is locally conformally flat. We also studied Ricci solitons for these spaces and concluded that any non-reductive homogeneous manifold with non-trivial recurrent curvature tensor is a steady Ricci soliton.